The work presents a comprehensive analysis of the current state of the issue concerning the dynamics of axisymmetric structures. A mathematical model, method, algorithm, and computer program for calculations on a computer have been developed to assess the dynamic characteristics (frequency, mode, and damping ratio of vibrations) of spatial axisymmetric structures, considering energy dissipation in the material using the hereditary Boltzmann-Volterra viscoelastic model in a three-dimensional setting.

The dynamic characteristics of specific spatial axisymmetric structures of the cooling tower type have been evaluated. It has been determined that for this type of structure, the lowest non-axisymmetric natural frequencies fall within the range of predominant earthquake frequencies.

It has been found that: accounting for dissipation in the material results in a slight reduction in the natural vibration frequencies of the structure and a weakly frequency-independent damping ratio; the installed stiffening rings at the top of the structure somewhat increase the non-axisymmetric natural vibration frequencies, while the bending frequencies of the structures decrease slightly.